By numerically solving the unforced and inviscid nonlinear barotropic vorticity equation through the quasi-Newton method, the steady free modes are obtained, which are very similar to the real flow fields, and their scatter diagram of (ψ, q) display segmented linear or nonlinear relations. From this scheme a range of free modes have been achieved, each corresponding to one of the atmospheric flow fields. In the study of changes in the western Pacific subtropical high (WPSH) as revealed by free modes it is discovered that the west-extension/northward jump and east-movement/southward withdrawal of WPSH for the free mode occur 5-10 days ahead of the changes in the high as shown in the 500 hPa geopotential height field. Besides,a standard mode technique is adopted to investigate the stability of the free modes, indicating that the faster the instable mode grows, the closer it comes to a quasi-steady state. Especially, the instable mode with its quasi-steady state growing the fastest bears a correspondence with the high in steady intensification, leading to the fact that the persistent strengthening of the high is likely to be caused by the instable free modes with the fastest growth that are of quasi-steady state, or experience long-period low-frequency variation.